This page is just for random little functions. That's it.
GODS stands for Graph of Dimensional states. It is similar to MiTerSkyArk's GOSS function, but more powerful.
GODS(N) is the number of combinations of an N x N x N ... N x N hypercube in N+1 dimensions, with N+1 colors.
The function is also equivalent to (N+1)^N^(N+1), which looks pretty neat.
For example, GODS(1) is 2, as there are 2 colors of a 1x1 grid.
GODS(2) = 6561, as it is 3^2^3 = 3^8.
GODS(3) ~ 5e48
GODS(4) ~ 5e715 (I'm using ExpantaNum to get these big number values)
GODS(100) ~ 10^10^202
GODS(10^100) ~ 10^10^10^102 (i call this number godsgol)
GODS(n) is still in the exponential range, but it's more like f^2[2](n)
The hyptorial is denoted with a ? symbol.
n? = n{n}n{n-1}n{n-2}...n^^n^n
You can put the ? BEFORE the n to do the WEAK hyptorial: ?n = n^n^^n...n{n-1}n{n}n. In other words, switch the order of the operations placed.
2? = 2^^2^2 = 2^^4 = 65536 (finally a function where 2 isn't degenerate)
3? = 3^^^3^^3^3 = 3^^^3^^27 = 3^^^3^3^3...3^3^3 with 28 3s in the whole expression.
?2 = 2^2^^2 = 2^4 = 16
?3 = 3^3^^3^^^3 = 3^3^^^4 by rules of pentation
?4 = 4^4^^4^^^4^^^^4 = 4^4^^4^^^^5 by rules of hexation
n? necessarily grows slower than n{n+1}n, but faster than n{n}n, so it's growth rate is around omega, and ?n clearly grows slower than n?, though I don't know the growth rate of it.